Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
Desmos, Inc., San Francisco, California 94103, USA.
Soft Matter. 2017 Mar 15;13(11):2201-2206. doi: 10.1039/c6sm02011a.
We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of the square of the strain tensor. This method of tracking corresponds to minimizing the stored energy in an elastic solid or the dissipated energy in a viscous fluid. Our energy-minimizing approach extends the advantages of particle tracking to situations where particle imaging velocimetry and digital imaging correlation are typically required. This approach is much more reliable than the standard squared-displacement minimizing approach for spatially-correlated displacements that are larger than the typical interparticle spacing. Thus, it is suitable for particles embedded in a material undergoing large deformations. On the other hand, squared-displacement minimization is more effective for particles undergoing uncorrelated random motion. In the ESI, we include a flexible MATLAB particle tracker that implements either approach with a robust optimal assignment algorithm. This implementation returns an estimation of the strain tensor for each particle, in addition to its identification.
我们描述了一种用于跟踪大位移粒子的方法。从在不同时间点采样的粒子位置列表开始，我们通过最小化所有粒子的轨迹的应变张量的平方的迹的和来分配粒子的身份。这种跟踪方法对应于在弹性固体中最小化存储能量或在粘性流体中最小化耗散能量。我们的能量最小化方法将粒子跟踪的优势扩展到通常需要粒子成像测速和数字图像相关的情况。对于大于典型粒子间间距的空间相关位移，这种方法比标准的平方位移最小化方法更可靠。因此，它适用于嵌入在经历大变形的材料中的粒子。另一方面，平方位移最小化对于经历不相关随机运动的粒子更有效。在 ESI 中，我们包含了一个灵活的 MATLAB 粒子跟踪器，该跟踪器使用稳健的最优分配算法实现了这两种方法。该实现除了标识外，还返回每个粒子的应变张量的估计值。
